Data-driven deconvolution

In this paper we study an automatic empirical procedure for density deconvolution based on observations that are contaminated by additive measurement errors from a known distribution. The assumptions placed on the density to be estimated are mild and apart from continuity do not include additional smoothness conditions. The procedure uses a class of deconvoluting kernel estimates and selects the smoothing parameter so as to minimize an estimate of integrated squared error over a discret set. The resulting estimator is shown to be asymptotically optimal both in the integrated squared error and mean integrated squared error sense. A simulation study is performed to examine the practical merit of the procedure.